Question

A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and height are in the ratio 5 : 12, write the ratio of the total surface area of the cylinder to that of the cone.

Answer 1

Given that

 r : h = 5 :12

i.e. r = 5x , h =12x

Since,

Right, circular cone and right circular cylinder have equal base and equal right.

Therefore,

The total surface area of cylinder `S_1 = 2pir (h + r)`

The total surface area of cone `S_2 = pir(l + r)`

`l = sqrt(r^2 + h^2)`

`= sqrt(25x^2 + 144x^2)`

`=sqrt(169x^2)`

`l = 13x`

Now,

`S_1/S_2 = (2pir(h + r))/(pir (l +r))`

      `= (2(h+r))/(l+r)`

`S_1 /S_2 = (2(12x + 5x))/(13x + 5x)`

      `=(2xx 17x)/(18x)`

`S_1 /S_2 = 17/9`

Hence,`S_1 : S_2 = 17 : 9`